The Ring Flip Process
Cyclohexane undergoes a conformational change known as the ring-flip process in which each axial
substituent becomes equatorial and each equatorial becomes axial. The substituents swap positions
because the carbon skeleton undergoes inversion with respect to a plane slicing through the center of the
ring. Those carbon atoms that were puckered up become puckered down, and vice versa.
The process can be viewed along
the perspective of the Newman
projection as shown here. Notice
the carbon bridge in front is
initially “down” but then is flipped
“up”. The equatorial substituents
twist into the axial positions and
the axial substituents twist into the
equatorial positions.
e
e
e
e
the substituents labeled
e (for equatorial)...
ring-flip
a
a
a
a
...move to the positions
labled a (for axial) during
the ring-flip process
The Minimum Energy Pathway (MEP)
We are about to discuss the atomic movements that bring about the ring-flip process. The description that follows is
detailed and requires concentration; it is best to build a physical model of cyclohexane and use it to understand the
ring-flip process. If you don’t have a model kit, study the web page listed at the bottom of this slide. Why so much
detail? Generalization of this particular example will provide insight into reactivity of other complicated processes
that we will encounter.
Throughout this discussion, don’t lose sight of the most
important point: the atomic movements follow the path of
least resistance on cyclohexane’s potential energy surface
(i.e., energy landscape). If we think of this surface as
mountain terrain in which height above sea level
corresponds to energy, then the pathway that describes the
ring-flip process is analogous to the route traveled by a
hiker who goes from one valley to the next via a “mountain
pass” (the mathematical name for the mountain pass is
saddle point - where a minimum in one direction crosses a
maximum in another). Change comes from an exact
process rather than by the molecule traveling along a
random excursion on its energy landscape. In other words,
there is a definite, well-defined path of least resistance and
this is the preferred pathway of change. This statement
holds true for most of the chemical change that we’ll
encounter in chemistry. We call the pathway along which
change occurs the Minimum Energy Pathway (MEP),
also known as the reaction coordinate. Let’s apply these
abstract ideas to the ring-flipping process of cyclohexane.
http://www.chem.ucalgary.ca/courses/351/Carey5th/Ch03/ch3-06.html
torsion 1
Cyclohexane’s Energy Landscape
torsion 2
The reason we’ve chosen to study cyclohexane’s ring-flipping
process in detail is because it teaches us the connection between a
MEP and its potential energy surface (we’ll use the terms
energy landscape and potential energy surface interchangeably).
The potential energy associated with cyclohexane’s
conformations is fairly well described as a function of just two
independent variables. These two variables are torsion angles of
any two bonds in the ring positioned directly across from one
another. Because of the molecule’s cyclical connectivity, the
other atoms are not entirely free to move independently of these
torsions. The carbon atoms in the diagram are represented as
colored circles so we can track the movement of individual atoms
along the reaction coordinate. (Note: that only two torsions
describe the process is a simplification; for a complete
description see: Dunitz, J. D. J. Chem. Educ. 1970, 47, 488).
The contour plot represents a portion of the 3D energy landscape for
cyclohexane (i.e., a potential energy surface). The x and y axes
correspond to torsion angles 1 and 2 while energy is given by the
contour lines (the z direction). The contour lines are equipotential
curves; a set of points having the same energy. The contour lines are
steps in energy, forming valleys (light color, low energy) and
mountain passes (dark color, high energy). The preferred pathway of
change (i.e., the MEP) connects one valley to another through a
saddle point. The saddle point is the transition state; the energy at
this point is the transition energy and the structure at this point is
called the transition structure (commonly given the symbol ‡).
Working
with
Models
1) Build a model of cyclohexane. Make all the axial substituents red atoms and all of the equatorial substituents blue atoms.
Place a piece of tape around one of the ring bonds and call this torsion 1. Then place a second piece of tape around the ring
bond that is directly opposite torsion 1. Call this bond torsion 2.
2) Grab the model by holding the two carbon atoms of torsion 1, one atom in your left hand and the other in your right.
3) Simultaneously rotate your hands in opposite directions. There are two ways to twist your hands in opposite directions
(i.e., you can either twist such that the axial substituents tip toward you or away from you). You’ll notice that one way
encounters resistance, while twisting in the other way is easy. Twisting about the easy way tips the axial substituents toward
you. Go ahead and twist about torsion 1 in the easy way until you cannot twist anymore. Your model is no longer in the chair
form. It is now a “twist conformation” of cyclohexane.
4) Now grab the model by holding the two carbon atoms of torsion 2, one atom in your left and the other in your right hand.
5) You’ll again notice that twisting in one way again encounters resistance, while twisting in the other way is easy. Twist
about torsion 2 in the easy way. Your model has returned to a chair form. The red atoms (formerly axial substituents) are
now in the equatorial positions. The blue atoms (formerly equatorial substituents) are now in the axial positions.
The Valley of the Twist Form
There is one more feature to cyclohexane’s
energy landscape, and it has to do with the valley
that separates ring-flipped chair forms.
The
region in between two chairs is called the valley
of the twist form. It is a minimum valley on
cyclohexane’s energy landscape. If there exists a
minimum point on an MEP between a starting
point and product we call this minimum an
intermediate. The twist form is thus an
intermediate on the ring-flip MEP.
The energy landscape at the right shows that the
valley of the twist form runs to the upper left
hand corner. This is a second MEP (colored
green) that converts one twist form into another.
This MEP passes through a saddle point
corresponding to the boat conformation of
cyclohexane. The boat form is placed in brackets
with a double dagger (≠) to symbolize that this
structure is a transition structure.
transition
structure
transition
structure
starting
conformation
intermediate
A MEP along the valley
of the twist form
boat form
twist form
twist form
For details see:
Leventis, N.; Hanna, S. B.; Sotiriou-Leventis, C.
J. Chem. Educ. 1997, 74, 813